1. Chapter 5 Types

2. 5-2 Topics in this Chapter Values vs. Variables Types vs. Representations Type Definition Operators Type Generators SQL Facilities

3. 5-3 Types A type is a set of values F/k/a (formerly known as) a domain Types can be system-defined or user-defined All types have associated operators Formally, this means that the operator can take the given type as a parameter For example integers can be passed to an addition operator but not a sub-string operator

4. 5-4 Values vs. Variables - Values A value is an individual constant It has no location in time or space A value is represented by encoding, which generates its appearance, which is spatial and temporal Appearances can occur in different times and spaces: they are manifold A value cannot be updated, for then it would be some other value: a value is immutable

5. 5-5 Values vs. Variables - Variables A variable is a holder for an appearance of a value It has location in time or space A variable can be updated, that is, it can hold another value A variable maintains its identity during the update: it is still the same variable

6. 5-6 Values vs. Variables Values can be simple or complex –Simple: integer, char –Complex: an XML document, a relation A value per se can have multiple appearances An appearance can have multiple encodings When we refer to a “value,” we often mean “an appearance of an encoding of a value”

7. 5-7 Values and Variables are Typed Every value has its immutable type Every variable has its immutable type, so that all its values will be of that type Every attribute of every relvar has its immutable type Operators have a type when operating, but this can be polymorphic in different contexts –e.g. = can operate on integers or characters, but not both at the same time

8. 5-8 Types and their Representations A type per se is idealized, conceptual, a model A representation (appearance) of the type is its implementation Sometimes a type is called an ADT – Abstract Data Type, but this is inherently redundant This logical and physical distinction is an aspect of data independence

9. 5-9 Types and their Representations - Scalar vs. Non-Scalar A scalar type is atomic and encapsulated –Integer, char, bool A non-scalar type is complex and user-visible –Name, address, employee, radiology image Values, variables, attributes, operators, parameters, expressions: all can be scalar or not, mutatis mutandis

10. 5-10 Types and their Representations - Possible Representations Let T be a scalar type The physical representation is hidden from the user Values of type T must have at least one possible representation, which is not hidden from the user The possible representation of a scalar type may have components, and if so, then at least one set of these must be visible to the user

11. 5-11 Types and their Representations - Possible Representations Each type has at least one POSSREP visible to the user in its declaration Each POSSREP includes two operators –Selector to specify a value for each representation –Ex.: QTY (100), QTY(N1 – N2) –THE_ to access each representation –Ex.: THE_QTY (Q), THE_QTY (Q1 – Q2), QTY cannot equal 100, because quantity is not an integer, if it has been declared as a type QTY can equal QTY(100)

12. 5-12 Type Definition TYPE WEIGHT POSSREP { D DECIMAL (5,1) CONSTRAINT D > 0.0 AND D < 5000.0 }; TYPE WEIGHT POSSREP LBS { L DECIMAL (5,1) CONSTRAINT L > 0.0 AND L < 5000.0 }; POSSREP GMS { G DECIMAL (7,1) CONSTRAINT G > 0.0 AND G < 2270000.0 AND MOD (G, 45.4) = 0.0 };

13. 5-13 Operators OPERATOR ABS (Z RATIONAL) RETURNS RATIONAL; RETURN (CASE WHEN Z > 0.0 THEN +Z WHEN Z < 0.0 THEN –Z END CASE); END OPERATOR;

14. 5-14 Operators OPERATOR REFLECT (P POINT) UPDATES P; BEGIN; THE_X (P) := - THE_X (P) ; THE_Y (P) := - THE_Y (P) ; RETURN; END; END OPERATOR; DROP OPERATOR REFLECT;

15. 5-15 Type Conversions QTY(100) converts an integer to a quantity THE_QTY (Q1) converts a quantity to an integer P# = ‘P2’ violates the rule that both sides of an assignment must be of the same type Compiler uses the P# selector implicitly to convert ‘P2’ from Char to P# a/k/a “Coercion” Coercion is not permitted

16. 5-16 Type Conversions Coercion is not permitted Explicit casting is permitted CAST_AS_CHAR (530.00) This is called strong typing: i.e., every value has a type, and the compiler checks to verify that operands are of the correct type for an operation –Can’t add weight to quantity, but can multiply them

17. 5-17 Type and Domain All types are known to the system The types in a database are a closed set Assignments and comparisons, ditto In a database system, a domain is a type, and thereby is an object class Hence we can speak about relations and objects simultaneously

18. 5-18 Type Generators a/k/a parameterized types, or templates ARRAY is a classic invocation of a type generator ARRAY can take in all sorts of types, and can return all sorts of other types VAR SALES ARRAY INTEGER [12]; ARRAY operators such as assignment, equality, THE_ work equally well with any valid type, i.e., a type known to the system

19. 5-19 SQL Facilities Built-in operators such as CHAR, NUMERIC, BLOB, BOOL… Mostly strong typing, but SQL will coerce FLOAT to NUMERIC, for example Supports two kinds of user-defined types: distinct types and structured types SQL does not support POSSREP – only one representation per type SQL does not support CONSTRAINTs

20. 5-20 SQL Facilities – Distinct Types CREATE TYPE WEIGHT AS DECIMAL (5,1) FINAL; For distinct types, SQL supports Selector and THE_ POSSREP not supported, so WEIGHT is always a DECIMAL Distinct types are strong, so you cannot use a comparison operator between the type and its underlying representation

21. 5-21 SQL Facilities – Structured Types CREATE TYPE POINT AS (X FLOAT,Y FLOAT) NOT FINAL; Uses operators in place of Select and THE_ Observe and mutate methods Structured types can be ALTERed or DROPped Tuples and relations are structured types

22. 5-22 SQL Facilities –Type Generators SQL includes three type generators: REF, ROW, ARRAY REFERENCE generates a reference ROW generates a set of fields ARRAY generates an array

23. 5-23 SQL Commands GROUP BY and HAVING By including a GROUP BY clause functions such as SUM and COUNT are applied to groups of items sharing values. When you specify GROUP BY region the result is that you get only one row for each different value of region. All the other columns must be "aggregated" by one of SUM, COUNT... The HAVING clause allows use to filter the groups which are displayed. The WHERE clause filters rows before the aggregation, the HAVING clause filters after the aggregation. If a ORDER BY clause is included we can refer to columns by their position.

24. 5-24 Orderby Command Select * from emp order by ename; SELECT ename, salary FROM emp WHERE salary > 1000 ORDER BY salary DESC Display Sum in Query. SELECT SUM(population), SUM(gdp) FROM bbc WHERE region = 'Europe‘; Distinct Command SELECT DISTINCT region FROM bbc

25. 5-25 Set Operators Set operators combine the results of two component queries into a single result. Queries containing set operators are called compound queries. They are fully described, including restrictions on these operators, in Operators OperatorReturns UNION - All rows selected by either query UNION ALL - All rows selected by either query, including all duplicates INTERSECT - All distinct rows selected by both queries MINUS - All distinct rows selected by the first query but not the second

26. 5-26 Max, Min Select max(sal) from emp; Select min(sal) from emp;